2. Find Solution using Gauss Forward formula

x	f(x)
310	2.4914
320	2.5052
330	2.5185
340	2.5315
350	2.5441
360	2.5563

x = 337.5

Solution:
The value of table for `x` and `y`

x	310	320	330	340	350	360
y	2.4914	2.5052	2.5185	2.5315	2.5441	2.5563

Gauss's forward method to find solution

`h=320-310=10`

Taking `x_0=330` then `p=(x-x_0)/h=(x-330)/10`

Now the central difference table is

`x`	`p=(x-330)/10`	`y`	`Deltay`	`Delta^2y`	`Delta^3y`	`Delta^4y`	`Delta^5y`
310	-2	2.4914
			0.0138
320	-1	2.5052		-0.0005
			0.0133		0.0002
330	0	2.5185		-0.0003		-0.0003
			0.013		-0.0001		0.0004
340	1	2.5315		-0.0004		0.0001
			0.0126		0
350	2	2.5441		-0.0004
			0.0122
360	3	2.5563

`x = 337.5`

`p = (x - x_0)/h = (337.5 - 330)/10 = 0.75`

`y_0=2.5185, Delta y_0=0.013,Delta^2y_(-1)=-0.0003,Delta^3y_(-1)=-0.0001,Delta^4y_(-2)=-0.0003,Delta^5y_(-2)=0.0004`

Gauss's forward interpolation formula is
`y_p=y_0+p Delta y_0 + (p(p - 1))/(2!) * Delta^2y_(-1) + ((p + 1)p(p - 1))/(3!) * Delta^3y_(-1) + ((p + 1)p(p - 1)(p - 2))/(4!) * Delta^4y_(-2) + ((p + 2)(p + 1)p(p - 1)(p - 2))/(5!) * Delta^5y_(-2)`

`y_(0.75) = 2.5185 + (0.75)(0.013) + ((0.75)(0.75 - 1))/(2) * (-0.0003) + ((0.75 + 1)(0.75)(0.75 - 1))/(6) * (-0.0001) + ((0.75 + 1)(0.75)(0.75 - 1)(0.75 - 2))/(24) * (-0.0003) + ((0.75 + 2)(0.75 + 1)(0.75)(0.75 - 1)(0.75 - 2))/(120) * (0.0004)`

`y_(0.75)=2.5185 +0.00975 +0.000028125 +0.0000054687 -0.000005127 +0.0000037598`

`y_(0.75)=2.52828`


Solution of Gauss's forward interpolation is `y(337.5) = 2.52828`

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